http://en.wikipedia.org/wiki/Error_propagation
http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm
Please review the link above for more
information and theory.
You can make S-plus compute partial
derivatives for you :
e.g: deriv(~ (W + log(x) / Y
),c("W","x","Y"),function(W,x,Y) NULL, formal=T)
Using the Partial derivatives and the variance
covariance matrix you can apply the formula:
http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55b.gif
Hope this helps,
Samer
Samer Mouksassi, Pharm.D.
Senior Associate Scientist,
Reporting and Analysis Services
Pharsight - A Certara™ Company
From: s-news-owner@lists.biostat.wustl.edu
[mailto:s-news-owner@lists.biostat.wustl.edu] On
Behalf Of Alan Hochberg
Sent: 2009-02-26 09:44
To: 'dorothy pang'; 's news'
Subject: Re: [S] Confidence
interval for transformed variables
Hi Dorothy,
If you want an actual formula for the
confidence limits, there is no simple answer to this, and it not only depends
on the shape of the distribution of the three variables, but it also depends
strongly on the correlations among the variables, i.e. how strongly they are
related to one another. Prepare for some Taylor series expansions and a lot of good
old-fashioned pencil scratching, for which this handy summary on means and
variances of ratios may come in handy:
http://www.stat.cmu.edu/~hseltman/files/ratio.pdf
Your alternative, assuming you have at
least several hundred values of each variable, is to make a bootstrap
estimate. To get started down that path, Google
“Bootstrapping” and check out the help for the S-plus
“bootstrap()” function.
Alan
Alan Hochberg
VP, Research
ProSanos Corporation
225 Market St. Ste. 502,
Harrisburg, PA 17101
Tel
717-635-2124 * Fax 717-635-2575
From:
s-news-owner@lists.biostat.wustl.edu
[mailto:s-news-owner@lists.biostat.wustl.edu] On
Behalf Of dorothy pang
Sent: Wednesday, February 25, 2009
10:33 PM
To: s news
Subject: [S] Confidence interval
for transformed variables
Dear all,
I have obtained 95% CI for variables X, Y and W, and would like to obtain the
95% CI for the following new variable:
A= W+(In X)/Y
Please may I seek advice on how to go about obtaining the 95% CI for the newly
derived variable A in Splus?
Thanks in advance.
Warm regards
Dorothy
What can you do with the new Windows Live? Find
out
